Sears Canada has lost significant market share in intensely competitive Canadian retail market, where Wal-Mart Stores and Read MoreTarget have been expanding.

Victor J. Blue | Bloomberg | Getty Images

Sears Holdings Corp. signage

Sears Holdings, which operates nearly 2,500 stores in the United States and Canada, said it would hire an investment bank to help explore alternatives for its stake in the Canadian company.

The operator of Sears department stores and the Kmart discount chain is trying to engineer a turnaround after suffering from declining sales since 2005, when Lampert merged the two U.S. chains in an $11 billion deal.

Sears Canada's shares, which have risen about 55 percent in the past year, closed at C$15.76 on Tuesday on the Toronto Stock Exchange. Sears Holdings' shares have fallen about 4.5 percent in the past year.